To begin with, a conventional multi-bean antenna device using a Rotman lens will be explained with its exploded perspective view illustrated in FIG. 11. In FIG. 11, the reference numeral (31) denotes a Rotman lens pattern whose details are illustrated in FIG. 12. In FIG. 12, the reference numerals (221), (222), - - - (22m) denote respective ones of a plurality of input ports for feeding electric power to a Rotman lens (1), and the reference numerals (231), (232), - - - (23n) denote respective ones of a plurality of output ports for extracting electric power in the Rotman lens (1). The reference numerals (241), (242), - - - (24n) denote respective ones of a plurality of antenna elements for radiating electromagnetic waves to space, and the reference numeral (205) denotes an array antenna having the plurality of antenna elements (241), (242), - - - (24n) arranged linearly. The reference numerals (261), (262), - - - (26n) denote respective ones of a plurality of feeder lines connecting respective ones of the output ports to respective ones of the antenna elements, and the reference numeral (207) denotes a line section comprised of the feeder lines (261), (262), (26n) having different lengths. The reference numeral (208) denotes a center line. This antenna device is line-symmetric with respect to the center line (208). The reference numeral (209) denotes an auxiliary line for indicating a position of one (221) of the input ports. The input port (221) is located in a direction at an elevation angle α with respect to the center line (208) when viewed from S2 which is an origin of an X-Y coordinate system. The reference numeral (210) denotes a straight line which is indicative of a spatial beam direction upon excitation of the input port (221), and oriented in a direction at an angle β with respect to a direction facing a front of the array antenna. In a primitive or basic design process, a Rotman lens is generally designed under a condition of β=α.
In the conventional antenna device configured as above, when one of the input ports (221), (222), - - - (22m) is excited, electric power is fed into the Rotman lens (201). The electric power in the Rotman lens (201) is extracted from each of the output ports (231), (232), - - - (223n), and transmitted to a corresponding one of the antenna elements (241), (242), - - - (24n) through a respective one of the feeder lines (261), (262), - - - (26n). Each of an excitation amplitude and an excitation phase of the array antenna (205) depends on which of the input ports (221), (222), - - - (22m) is excited, and the spatial beam direction depends on the excitation phase of the array antenna (205).
In the conventional Rotman lens pattern illustrated in FIG. 12, the input ports (221), (222), - - - (22m) are arranged on an arc having a radius R from a center located at a focal point S1 of the Rotman lens. The origin S2 of the X-Y coordinate system is represented by an intersecting point of the center line (208) with a curve segment having the output ports (231), (232), - - - , (23n) arranged thereon. S3 indicates an intersecting point of the center line (208) with a curve segment having the input ports (221), (222), - - - , (22m) arranged thereon. An x coordinate and a y coordinate of each of the output ports (331), (332), - - - (33n), and an electrical length w of each of the feeder lines (261), (262), - - - (26n), are expressed in the following Formulas 1 to 3, respectively:x=[2w(1−g)−b02η2]/2(g−a0)  (1)y=η(1−w)  (2)w=[−b−√{square root over ((b2−4ac))}]/2a  (3)
In the above Formulas 1 to 3,                g=G/F, η=Ln/F, a0=cos α, b0=sin α,        a=1−η2−[(g−1)/(g−a0)]2,        b=2g(g−1)/(g−a0)−[(g−1)/(g−a0)2]b02η2+2η2−2g, and        c=gb02η2/(g−a0)−b04η4/[4(g−a0)2]−η2.        
Further, the radius R is expressed in the following formula:R=[(Fa0−G)2+F2b02]/[2(G−Fa0)]  (4)
In the Formula 4, G is a size of the Rotman lens defined by a distance between S2 and S3. Further, F is a distance between the input port (221) and S2, and 2 Ln is an aperture length of the array antenna (205). In the basic design process, it is commonly considered that it is desirable to set η approximately in the following range: 0.8<η<1, i.e., set F in a range of about 1 to 1.25 times Ln, and set g to about 1.137, under a defined condition of β=α, in view of an advantage of being able to reduce an error in excitation phase at each of the output ports (231), (232), - - - (23n).
Meanwhile, as means for achieving a pencil beam antenna capable of radiating two orthogonally polarized waves in a single antenna unit, a structure formed by electromagnetically coupling two-layer triplate antennas as illustrated in FIG. 13 is considered to be effective.